The Dornbusch Sticky-Price Monetary Model (SPMM) and Austrian Insights

of two separate monetary standards, this “condition” stands just for a meaningless truism. It holds for all exchange rates and for all prices, whatever they are. Moreover, we have already argued in one of the sections above⁶¹ that change in the price of a good could have an impact on the exchange rate. This impact depends just on the preferences of holders of the currency, whether they understand the good the price of which is changed as a complement or rather a substitute to goods purchasable by the other currency.

This section discussed one part of the Austrian analysis of exchange rate determination, namely its equilibrium purchasing power condition. We have showed that while this condition does have something to say for the case of parallel currencies, it brings no additional knowledge to the case of two separate monetary standards that is of our interest. This branch of the analysis is not useful for the purposes it claims itself to be.

“Equilibrium exchange rate” is undoubtedly one of the core concepts of this framework. Not omitting the importance of its clarification, we leave it for the later stage of the discussion.

The first question to be posed concerns exchange rate’s departures from this equilibrium represented by “ē – e”⁶⁵. The answer is supposed to be given by the uncovered interest rate parity (UIP)⁶⁶. This is assumed to hold instantaneously⁶⁷. It is therefore the difference between the world and the domestic interest rate that explains the existence of disequilibrium exchange rates.

And why do the interest rates differ in respect to each other? This is due to assumptions concerning flexibility of the domestic “money market” – the determinant of r; and the domestic “goods market” – where p is settled⁶⁸. Whereas the former is “flexible”, the later one is “sticky”. In fact, interest rate serves as a “buffer” for people with too high or too low cash balances in respect with slowly responding prices. It therefore looses its connection with the world interest rate. The mutual and always present relationship between r and p is formulated as: –λr + Φy = m –p⁶⁹. Whenever other variable (y or m) changes⁷⁰, it is r, out of r and p, that is supposed to bring the market into the short-run equilibrium: p is assumed to respond only after some lag. Increases or decreases in the money supply thus have to be answered by changes in the interest rate in the short run: the former by decreases in r in order to make people keep additional cash balances and the later by increases in r, making lower cash balances to be regarded as sufficient.

The existence of the difference between the spot exchange rate and the equilibrium exchange rate therefore springs from the fact of sticky prices. If the domestic prices are too low compared to their equilibrium values, spot exchange rate overshoots its ē: lowered interest rate, compensating not-yet-increased p, induces outflow of funds unless sufficient appreciation of the currency is expected⁷¹. Mutatis mutandis, if the domestic prices are too high compared to their equilibrium values, spot exchange rate undershoots its ē: increased r,

65 Exchange rate is here, as usually, stands for the number of units of the domestic currency per unit of the foreign currency.

66 This is expressed by the formula r = r* + θ(ē – e), which in other words means that „... the expected rate of depreciation of the spot rate is proportional to the discrepancy between the long-run rate and the current spot rate“ Dornbusch (1976, p. 1163).

67(ibid., p. 1163).

68 (ibid., p. 1166)

69 (ibid., p. 1163, p. 1165).

70 Following the first part of Dornbush (1976, pp. 1161-1171), Pilbeam (1998), Sarno and Taylor (2003) – except the last paragraph p. 107, we will omit the analysis of changes in product in this work, however.

71 Dornbusch (1976, pp. 1168-1171).

compensating not-yet-decreased p, induces inflow of funds unless sufficient depreciation of the currency is expected^{72, 73}.

The paragraphs devoted to the “money market” provided us with the “dynamics” of the model. The “goods market” provides us with two bases lacking in the previous theorizing:

first, the nature of the price level’s lags in attaining its run equilibrium; second, the long-run exchange rate equilibrium.

The first point is determined by coefficient π of the following formula: = π (u + δ(e – p) + y (γ – 1) – σr)⁷⁴.

p&

The second point is determined accordingly: ē = p+ 1/δ (σr* – u – y (γ – 1))⁷⁵.

Now, to what extent and in what respect is the above compatible with the Austrian approach?⁷⁶

Both sides – Dornbuschian and Austrian, accept in some way or another the UIP. For a Dornbuschian, UIP stands for an omnipresent condition: given the foreign interest rate and expected value of the currency, differential between present r* and present r, has to be in accordance with the expected change in the value of the currency. Austrian, on the other hand, first points out e that he wants to explain. Then he chooses relevant r, relevant (expected) future exchange rate, and relevant r* - all in different time points so that actual arbitrage could be assumed to take place, and only then analyzes e. The basic difference between both approaches in case of UIP could be then formulated as follows: while one explains the world with relationship of interdeterminance, the other chooses the prism of causality instead.

The Austrian approach to the theory of money and interest⁷⁷ suggest that the case of the

“money market”⁷⁸ will be more problematic for mutual consistence of implications of both

72 On the decrease in the amount of money see Sarno and Taylor (2003, p. 104, p. 107).

73 To put this notion into the formula: e = ē – 1/ (λθ) (p –p)).

74 Dornbusch (1976, p. 1164)

75 (ibid., p. 1165)

76 The usual Austrian rejoinder in this case would be at first place related with methodological comments against mathematical and mechanical determinist formulas in economics. This line will not be presented here, on this, see for example Mises (1996, esp. pp. 350-357).

investigated theories. The questions of our concern will be represented by relations between interest rate, money supply and price level.

Money supply and price level: Austrians accept that increase (decrease) in the amount of money tends to decrease (increase) its marginal utility for the people concerned. As a consequence, the prices will tend to be finally higher (lower) than otherwise⁷⁹. These price changes occur only in a step-by-step and uneven manner, however, they are in no exact functional-numerical way related to the change in the amount of money. Nevertheless, from the point of Dornbusch (1976), the important fact is that price changes occur with lags in relation to the time-point when the amount of money is changed, and it is clear that Austrians are in agreement with this conclusion.

Money and interest rate: It is assumed in the discussed model that “[t]he demand for real money balances is assumed to depend on the domestic interest rate and real income[.]”⁸⁰ In the sticky-price situation, higher (lower) cash balances, as a consequence of increase in m, will necessary lead r to be lower (higher) than otherwise. For Dornbuschians, interest rate is then a kind of a buffer – its flexibility prevents “explosion” of the system due to inflexible prices when the pressure of the new money arises. Austrians take a different position. There are no “pressures” that are to be “solved” when new money is poured in. Prices usually appear to be inflexible because they naturally rise in a step-by-step manner – additional demand spreads only gradually throughout the economy. And there is no a priori reason why the demand for future goods in relation with present goods should be affected first. However, on empirical grounds, since the mechanism by which new money is usually poured in (taken from) is based on the changes in the interest rate, increases (decreases) in the money supply are usually accompanied with interest rate being lower (higher) than otherwise. In other words, the relationship of money supply and interest rate put into picture by Dornbusch is feasible in the Austrian framework⁸¹, although within completely different tenets.

77 For the general treatment of the theory of money cf. Mises (1971). For a complex analysis of the topic of interest rates see Mises (1996, pp. 479-537), Rothbard (2004, pp. 13-17, pp. 319-451). For the comprehensive review of the Austrian interest literature cf. Hülsmann (2002).

78 It is supposed to hold here: –λr + Φy = m – p

79 The price level, depending on the way that it is measured will then consequently in a step-by-step manner tend to be higher (lower) than otherwise.

80 Dornbusch (1976, p. 1163) (emphasis added).

81 It should be added however that these changes in the interest rate are the causes for malinvestments and business cycles. For the „money-interest rate-business cycle“ mechanism see for example: Mises (1996, pp. 538-586); Rothbard (2004, pp. 989-1021).

Interest rate and price level: The important point was already raised in the previous paragraph – although Austrians do not agree with the Dornbuschian relationship between changes in the price level and changes in the interest rate, they agree that the consequence of change in the amount of money is most likely to affect the interest rate first and other fundaments only later.

Concerning the “goods market” – the determinant of price level lags and equilibrium/expected exchange rate determination, there is not much use of it for Austrians and they do not need it.

Lags of the price level are not important here at all since, as it was showed, they are not necessary for explanation of the relationship between r and m. Expected exchange rate, decisive for UIP, depends on the future valuations of the holders or potential holders of the currency in question.

The last question to be settled in this section concerns potential reconciliation of the overshooting model and the Austrian framework. It is clear that both of them represent two different worlds. Despite of this fact, however, the basic idea of the former is to an important extent relevant for the later. Let us take an example of an increase in m, leading r to be actually lower than otherwise in respect with the expected r* attainable by arbitrage⁸². Now, let us say that this very same increase in m will lead the future exchange rate to be higher than otherwise, i.e., that the domestic currency depreciate. The present exchange rate that is of our interest, represented by ER1 in the respective means-ends diagram below, will not only be driven higher by present holders of the domestic money due to higher ER2. It will have to be even higher than ER2 in order to compensate lowered r. Overshooting of ER1 in respect with ER2 thus appears.

ER1 r* ER2

foreign money future foreign repaid loan ^domestic _money money

domestic money

Figure 24: Austrian theory of exchange rates and overshooting

In case of the decrease in the amount of money leading to the counterfactual decrease in the exchange rate and counterfactual increase in the interest rate, on the basis of the previous reasoning, corresponding undershooting appears in the picture. The major difference compared to the Dornbusch’s model concerning the conclusions is that it is not the

82 The arbitrage would go in a way: first, borrow in the domestic country at r. Second, exchange this money for another currency. Third, lend them at the foreign interest rate r*. Fourth, after the period of time – exchange received foreign money for domestic currency. Fifth repay the loan.

equilibrium exchange rate that serves as the basis for overshooting or undershooting. Rather it is the expected future exchange rate.

Three addendums are to be made in the end of this section. First, it was its task to put both approaches against each other – Austrian and Dornbuschian, and contrast the mutual differences springing from their causal point of view, on the one hand, and deterministic point of view, on the other hand. Second, it was showed that despite of the undisputable differences, it is still possible to enrich one approach thanks to reasoning of the other. Third, the supposed reconciliation that was brought above in the previous paragraph should be understood as the beginning, not the end, of the chain of problems. It just represents an important insight worth of considering for an Austrian economist. Elaboration of the set of springing additional problems has to be dealt with at the other place⁸³.